#from John Stembridge F4 # point representatives from cells that are psd in all irreps face {1, 2, 3, 4} [0, 0, 0, 0, 0] face {2, 3, 4} [1, 0, 0, 0] {} {1} {23} [0, 0, 0, 0, 1] face {1, 3, 4} [0, 1, 0, 0] {} {2} {13} [0, 0, 0, 0, 1] face {3, 4} [1, 1, 0, 0] {} {1, 2} {5} [0, 1/2, 0, 0] {5} {13} {21} [0, 0, 0, 1, 1] face {1, 2, 4} [0, 0, 1/2, 0] {3} {6} {22} [0, 0, 0, 0, 1] face {2, 4} [1/4, 0, 3/8, 0] {6, 11} {9} {22} [0, 0, 0, 1, 0] face {1, 4} [0, 0, 0, 0, 0] face {4} [1/4, 1/2, 1/4, 0] {5, 7} {6, 11} {9} [0, 0, 0, 1, 0] face {1, 2, 3} [0, 0, 0, 1] {} {4} {10} [0, 0, 0, 1/2] {4} {10} {} [0, 0, 0, 0, 2] face {2, 3} [1, 0, 0, 1/2] {4} {1, 10} {15} [1/4, 0, 0, 3/8] {10, 15} {14} {23} [1/2, 0, 0, 1/2] {1, 4} {10, 15} {14} [0, 0, 0, 1, 2] face {1, 3} [0, 1, 0, 1] {} {2, 4} {12, 13} [0, 1/2, 0, 1/2] {2, 4} {12, 13} {10, 20} [0, 1/4, 0, 3/4] {4, 13} {12} {10, 20} [0, 1/3, 0, 1/3] {12, 13} {10, 20} {17} [0, 0, 0, 1, 3] face {3} [1, 1, 0, 1] {} {1, 2, 4} {5, 12} [1/2, 1/2, 0, 1/4] {1, 12} {5, 10} {13, 15} [1/3, 1/3, 0, 1/3] {5, 12} {10, 13, 15} {14, 20} [3/8, 1/4, 0, 3/8] {12, 13} {10, 15} {14, 20} [0, 1/4, 0, 1/4] {14, 20} {17} {21} [1/8, 1/4, 0, 3/8] {13, 15} {10, 20} {14} [1/4, 1/4, 0, 1/4] {10, 13, 15} {14, 20} {17} [0, 0, 1, 4, 2] face {1, 2} [0, 0, 1/4, 0] {24} {19} {} [0, 0, 1/4, 1/4] {16} {10, 22} {24} [0, 0, 0, 1, 1] face {2} [1, 0, 1/2, 1/2] {3, 4} {1, 6, 8} {11, 16} [1/2, 0, 1/4, 1/4] {11, 16} {9, 10, 15} {18} [1/3, 0, 1/3, 1/3] {6, 8, 11} {9, 15, 16} {10, 18} [1/4, 0, 1/4, 1/4] {9, 15, 16} {10, 18} {14, 22} [1/8, 0, 7/32, 0] {24} {19} {23} [1/8, 0, 7/32, 7/32] {10, 18} {14, 22} {24} [0, 0, 1, 2, 3] face {1} [0, 1/8, 5/16, 1/8] {13, 16} {10, 20} {17, 22} [0, 1/4, 0, 1/8] {19} {21} {} [0, 1/8, 5/32, 9/32] {20} {10, 22} {17} [0, 0, 1, 2, 0] face {} [1, 1, 1, 1] {} {1, 2, 3, 4} {5, 7, 8} [1/2, 1/2, 1/4, 3/4] {1, 4, 7} {5, 6, 8} {11, 12} [3/4, 0, 1/4, 1/4] {5, 16} {10, 11} {9, 15} [3/8, 1/4, 1/4, 1/8] {11, 16} {10, 15} {9} [1/4, 1/2, 1/8, 1/8] {11, 16} {9, 10, 15} {13, 18} [1/4, 1/2, 1/4, 1] {5, 7} {4, 6, 11} {8, 9} [1, 1/2, 1/4, 1/4] {7, 8} {1, 6, 12} {5, 16} [5/12, 1/6, 1/8, 7/24] {9, 16} {10, 13, 15} {18} [11/24, 1/12, 1/8, 1/3] {13, 16} {10, 15} {18} [1/8, 5/16, 1/8, 7/16] {9, 12} {13, 15, 16} {10, 18} [1/4, 0, 1/4, 1/2] {12, 13} {15, 16} {10, 18} [1/4, 3/8, 1/4, 1/8] {6, 11, 12} {15, 16} {9, 10} [1/4, 1/4, 1/4, 1/4] {6, 11, 12} {9, 15, 16} {10, 13, 18} [1/8, 1/8, 5/16, 1/8] {9, 15, 16} {10, 13, 18} {14, 20} [1/4, 1/8, 3/16, 1/4] {13, 15, 16} {10, 18} {14, 20} [0, 1/8, 1/8, 1/8] {24} {19} {21} [0, 7/16, 0, 0] {19} {} {21} [1/8, 1/6, 1/8, 7/24] {13, 18} {10, 20} {14, 22} [1/8, 5/24, 1/8, 5/24] {10, 13, 18} {14, 20} {17, 22} [1/4, 1/4, 0, 0] {19} {21} {23} [1/8, 1/12, 1/8, 1/3] {20} {10, 22} {14} [1/8, 1/8, 1/8, 1/4] {10, 20} {14, 22} {17} [0, 1/4, 1/8, 1/8] {14, 20} {17, 22} {24} [1/4, 0, 0, 1/4] {21} {23} {} [0, 0, 0, 0] {23} {} {} [2, 3, 11, 8, 1] 2 3 4 2 + 3 q + 14 q + 22 q + 18 q # representatives from the maximal psd cells # Format: fund.wt.coords co-dim J <1 =1 >1 [0, 0, 0, 0] 0 {} {23} {} {} [0, 1/4, 1/8, 1/8] 2 {} {14, 20} {17, 22} {24} [1/8, 1/8, 1/8, 1/4] 2 {} {10, 20} {14, 22} {17} [1/8, 1/12, 1/8, 1/3] 2 {} {20} {10, 22} {14} [1/8, 5/24, 1/8, 5/24] 2 {} {10, 13, 18} {14, 20} {17, 22} [1/8, 1/6, 1/8, 7/24] 2 {} {13, 18} {10, 20} {14, 22} [0, 7/16, 0, 0] 0 {} {19} {} {21} [1/4, 1/8, 3/16, 1/4] 2 {} {13, 15, 16} {10, 18} {14, 20} [1/4, 3/8, 1/4, 1/8] 2 {} {6, 11, 12} {15, 16} {9, 10} [1/4, 0, 1/4, 1/2] 2 {} {12, 13} {15, 16} {10, 18} [11/24, 1/12, 1/8, 1/3] 2 {} {13, 16} {10, 15} {18} [1, 1/2, 1/4, 1/4] 3 {} {7, 8} {1, 6, 12} {5, 16} [1/4, 1/2, 1/4, 1] 3 {} {5, 7} {4, 6, 11} {8, 9} [3/8, 1/4, 1/4, 1/8] 2 {} {11, 16} {10, 15} {9} [3/4, 0, 1/4, 1/4] 2 {} {5, 16} {10, 11} {9, 15} [1/2, 1/2, 1/4, 3/4] 3 {} {1, 4, 7} {5, 6, 8} {11, 12} [1, 1, 1, 1] 4 {} {} {1, 2, 3, 4} {5, 7, 8} [1, 1, 0, 1] 4 {3} {} {1, 2, 4} {5, 12}